What is (\partial)/(\partial y)(x^2y+y^3) ?

The answer to (\partial)/(\partial y)(x^2y+y^3) is x^2+3y^2

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(\partial)/(\partial y)(x^2y+y^3)

\frac{\partial}{\partial y} (x^{2} y + y^{3})

x^{2} + 3 y^{2}

Solution steps

\frac{\partial}{\partial y} (x^{2} y + y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (y^{3})

\frac{\partial}{\partial y} (x^{2} y) = x^{2}

\frac{\partial}{\partial y} (y^{3}) = 3 y^{2}

= x^{2} + 3 y^{2}

What is (\partial)/(\partial y)(x^2y+y^3) ?
The answer to (\partial)/(\partial y)(x^2y+y^3) is x^2+3y^2